This study presents a static analysis of laminated composite doubly curved shells using a refined kinematic model with polynomial and non-polynomial functions. In particular Maclaurin, trigonometric, exponential and zig-zag functions are employed. Refined models are based on the Equivalent Single Layer theories and obtained by using Carrera Unified formulation. The shell model is subjected to different mechanical loading such as bi-sinusoidal, uniform and point load. The governing equations are derived from the principle of virtual displacement and solved via Navier-Type closed form solutions. The results are compared with Layer-wise and higher-order shear deformation solutions available in the literature. It is shown that refined models with non-polynomial terms are capable of accurately predicting the through-the-thickness displacements and stress distributions with a low computational effort.